The determination of natural frequencies of （自然频率的决心）.pdf

International Journal of Mechanical Sciences 43 (2001) 1731–1746 The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution a ; ∗ a b G.W. Wei , Y.B. Zhao , Y. Xian a Department of Computational Science, National University of Singapore, Singapore 117543, Singapore b School of Engineering and Industrial Design, University of Western Sydney, Penrith South DC NSW 1797, Australia Received 23 March 2000; received in revised form 29 January 2001 Abstract This paper introduces the discrete singular convolution algorithm for vibration analysis of rectangu- lar plates with mixed boundary conditions. A unied scheme is proposed for the treatment of simply supported, clamped and transversely supported (with nonuniform elastic rotational restraint) boundary conditions. The robustness and reliability of the present approach are tested by a number of numerical experiments. All results agree well with those in the literature. ? 2001 Elsevier Science Ltd. All rights reserved. Keywords: Discrete singular convolution; Vibration analysis; Mixed boundary condition; Nonuniform boundary condition; Rectangular plate 1. Introduction Plates with mixed boundary conditions are key components in civil and mechanical engineer- in gand industrial design. Although theoretical analysis is valuable for providin gbasic under- standing, in general, there is no analytical solution to the problems of vibration and bucklin